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Article
Mathematics, Interdisciplinary Applications
Yanqiu Li et al.
Summary: The dynamics of a general Selkov-Schnakenberg reaction-diffusion model is investigated, including the stability of the equilibrium and the existence of bifurcations. Turing and Turing-Hopf bifurcations due to diffusion of the model are demonstrated, and the bifurcation diagram and spatial-temporal patterns are obtained. Numerical simulations show the emergence of homogeneous periodic, inhomogeneous, and inhomogeneous periodic solutions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
Summary: In this study, the existence of steady states, bifurcations, and spatiotemporal patterns are investigated for a diffusive predator-prey model. The nonexistence and existence of nonconstant steady states are justified using priori estimates, Poincare inequalities, and Leray-Schauder degree, respectively. The weakly nonlinear analysis is employed to establish the amplitude equations and various complex pattern solutions are identified from these equations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
Summary: In this paper, we investigate the role of prey-taxis in an ecological model. The local stability of the positive equilibrium and the occurrence conditions of the steady state bifurcation are given. By treating the prey-taxis constant e as the bifurcation parameter, we confirm the model possesses the steady state bifurcation at e =ekS for k & ISIN; N0/{0}. Numerical experiments show the stable bifurcating solution.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yong Wang et al.
Summary: This paper investigates the complex spatiotemporal dynamical behaviors of a diffusive predator-prey system with Michaelis-Menten type functional response and linear harvesting. Firstly, the necessary and sufficient critical conditions for Turing instability are derived in a novel way. Then, the existence conditions of codimension-1 Turing bifurcation, Hopf bifurcation, codimension-2 Turing-Turing bifurcation, and Turing-Hopf bifurcation are established. The detailed bifurcation set is obtained by calculating the amplitude equation with the method of the multiple time scale near the Turing-Hopf bifurcation. Numerical simulations verify the existence of nonconstant steady-state solutions, spatially homogeneous periodic solutions, and spatially inhomogeneous periodic solutions. These investigations provide insights into the effect of diffusion and harvesting on the dynamic behavior of the system and reveal the mechanism of spatiotemporal complexity in the diffusive predator-prey system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Mengxin Chen et al.
Summary: In this paper, a diffusive predator-prey system with network connection and harvesting policy is analyzed. The stability and dynamical behaviors of the system are explored, showing that the networked system exhibits distinct characteristics compared to the model without network structure.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Jafar Al-Omari et al.
Summary: A new delayed predator-prey model with stage-structure and harvesting on prey and predator has been proposed. The dynamics of the model largely depends on the harvesting efforts on the two species and the specific form of the birth and death functions. The study investigates the system's dynamical behavior in terms of local stability of each feasible equilibrium, global stability, and persistence.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Multidisciplinary
Renji Han et al.
Summary: This study investigates a generalist predator-prey model with nonlinear cross-diffusion, prey refuge and ratio-dependent functional response. The refuge parameter plays a key role in the dynamics of the model, influencing uniform persistence, stability of equilibria, Turing instability space and more. The study also compares the stabilizing effects of refuge depending on prey and refuge depending on both species. Numerical simulations reveal the growth of spatiotemporal patterns controlled by prey refuge and self- and cross-diffusion, including spots, stripes, mixtures and more. This proposed model contributes to the field of ecology with its richness and complexity.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Biology
Joydeb Bhattacharyya et al.
Summary: There is a global decline in marine fish abundance due to unsustainable harvesting. An effective harvesting policy can protect overfished populations from extinction. This study uses a mathematical model to explore an effective harvesting policy for herbivorous fish, focusing on their anti-predator behavior in the presence of invasive fish. The model considers the density-dependent refuge protection and the continuous threshold harvesting policy, and investigates the existence and stability of steady-state solutions and the bifurcations of the model. The study highlights the importance of herbivorous fish apprehension and fishing efforts in the system's stability, and also discusses subsidies and tax policies for sustainable fishery management. Numerical simulations are used to compare different harvest policies for ecologically sustainable and economically viable outcomes.
JOURNAL OF BIOLOGICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Milos Dolnik et al.
Summary: This study investigated the impact of discrete domain discontinuities on Turing pattern formation and discovered that obstructions significantly affect pattern formation and lead to novel pattern morphologies. The findings provide guidance for future numerical and experimental studies and offer new insights into biological pattern growth and formation.
Article
Mathematics, Interdisciplinary Applications
Ronobir Chandra Sarker et al.
Summary: In this article, the Weyl differential operator is used to study pattern formation among species with superdiffusive movement in space. The relationship between the wavenumber of the Turing pattern and the superdiffusive exponent is analyzed and verified by numerical simulation. The results show that the Turing pattern undergoes only quantitative changes for varying superdiffusive exponents.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mechanics
Renji Han et al.
Summary: This research focuses on the combined effect of cooperative hunting and prey refuge in a predator-prey model. The study confirms that the competition between hunting cooperation and prey refuge can determine the dynamics of the system. The findings demonstrate that when the hunting cooperation factor exceeds the prey refuge coefficient, both Hopf and Turing bifurcations occur. Additionally, a distinct Turing instability mechanism emerges when the prey diffusivity exceeds that of the predator.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Mathematics, Applied
Yue Liu et al.
Summary: This study investigates pattern formation behind a wave of competency using Turing's diffusion-driven instability model. The results show that wave speed has an impact on pattern formation, with slower speeds leading to peak splittings and higher speeds resulting in peak insertions. In two spatial dimensions, different wave speeds lead to the formation of perpendicular or parallel stripes.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematical & Computational Biology
Lakshmi Narayan Guin et al.
Summary: The paper investigates a reaction-diffusion predator-prey model incorporating prey refuge and harvesting, analyzing asymptotic stability and bifurcation conditions to discuss the spatiotemporal dynamics of the system. The results suggest that the cooperation of refuge and harvesting plays a crucial role in controlling spatial pattern formation of the species. Computer simulations reveal typical dynamics of population density variation within the Turing space, including isolated groups like spots, stripe-spot mixtures, and labyrinthine patterns.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
Summary: This paper investigates the Leslie-Gower type predator-prey system with the ratio-dependent Holling III functional response and Neumann boundary conditions. The existence of the codimension-two Turing-Hopf point is identified, and amplitude equations are derived using weakly nonlinear analysis to explore the spatiotemporal dynamics near the C2THP. The temporal patterns, hexagonal patterns, and plane wave patterns can be presented through amplitude equations, along with the sufficient conditions of their existence and stability.
CHAOS SOLITONS & FRACTALS
(2021)
Review
Multidisciplinary Sciences
Shigeru Kondo et al.
Summary: Skin patterns are the first example of Turing patterns in living organisms, with research revealing principles of pattern formation at molecular and cellular levels. Contrary to classical reaction-diffusion models, real skin patterns are established by autonomous migration and proliferation of pigment cells mediated through direct cell-cell interactions. Various studies are underway to adapt mathematical models to experimental findings in skin pattern research for potential applications in other autonomous pattern formation phenomena.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
Xiang-Ping Yan et al.
Summary: This paper investigates a modified Leslie-Gower delayed reaction-diffusion predator-prey model with prey harvesting of Michaelis-Menten type and under homogeneous Neumann boundary condition. The global asymptotic stability of the positive constant steady state is further analyzed and an existing global stability result is enhanced.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Renji Han et al.
Summary: In this study, a predator-prey interacting model with prey refuge in proportion to both the species and Beddington-DeAngelis functional response is proposed and examined. The coefficient of refuge plays a significant role in modifying the system dynamics and mediating the population permanence, stability of coexisting equilibrium, and Turing instability parameter space. Numerical simulations show complex dynamics including prey refugia, self-diffusion controlling spatiotemporal pattern growth, and various spatial patterns like spots, stripes, mixtures, and rings.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Yong Yao
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
Article
Mathematics, Applied
Mengxin Chen et al.
APPLIED MATHEMATICS AND COMPUTATION
(2020)
Article
Mathematics, Interdisciplinary Applications
Mengxin Chen et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2020)
Article
Mathematics, Applied
Hyundong Kim et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Physics, Multidisciplinary
Lili Chang et al.
NEW JOURNAL OF PHYSICS
(2019)
Article
Engineering, Multidisciplinary
Malay Banerjee et al.
APPLIED MATHEMATICAL MODELLING
(2018)
Article
Ecology
Mengxin Chen et al.
ECOLOGICAL COMPLEXITY
(2018)
Article
Mathematics, Interdisciplinary Applications
Zhichao Jiang et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2018)
Article
Mathematics, Interdisciplinary Applications
Fengrong Zhang et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2018)
Article
Engineering, Mechanical
Lakshmi Narayan Guin et al.
NONLINEAR DYNAMICS
(2017)
Article
Mathematics, Applied
R. P. Gupta et al.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2017)
Article
Mathematics, Applied
Dongmei Xiao
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2016)
Article
Environmental Sciences
Amit Sharma et al.
MODELING EARTH SYSTEMS AND ENVIRONMENT
(2016)
Article
Mathematics, Applied
Hong-Bo Shi et al.
APPLIED MATHEMATICS AND COMPUTATION
(2015)
